一维改进分形海面模型及海谱分析

针对经典分形模型的功率谱在空间波数小于基波波数时不能满足正幂率的问题,提出了一种统计模型和归一化带限Weierstrass分形模型相结合的一维粗糙海面模型,得到改进分形表面功率谱,并且和PM谱进行了对比,对分形维数、频率幅度尺度因子、风速等参量对一维海面轮廓的影响做了进一步分析.研究表明:在不同风速下表面功率谱和PM变化趋势是一致的,证明了改进方法的正确性.海面形状具有大尺度涌浪和小尺度张力波的特性,并且统计模型和分形模型的性质在改进模型中依然适用,验证了模型的合理性.

A one-dimensional improved fractal model of sea surface and sea spectrum evaluation

As to the problem that the fractal spectrum can not satisfy the positive power law when wave numbers are smaller than the fundamental wave number,an improved 1D fractal model is proposed.This proposed model is a combination of statistical sea model and normalization band-limited Weierstrass-Mandelbrot(WM) fractal sea model.The improved fractal sea wave spectrum is derived,and the results are compared with the PM sea wave spectrum.A further study on improved fractal model’s fractal dimension,the frequency and amplitude factor and wind speed affecting the sea-surface is made.The analysis illustrates that improved fractal sea wave spectrum shows good agreements with PM spectrum’s change trend for different wind speed,which proves the correctness of the improved method.Sea surface has characters of large-scale turbulent waves and micro-scale capillary wave,while statistical model and fractal model’s characters can be still applied in improved fractal model.The rationality of improved fractal model is validated.